On the value of exposure and secrecy of defense system: first-mover advantage vs. robustness

It is commonly accepted in the literature that, when facing with a strategic terrorist, the government can be better off by manipulating the terrorist's target selection with exposing her defense levels and thus moving first. However, the impact of terrorist's private information may significantly affect such government's first-mover advantage, which has not been extensively studied in the literature. To explore the impact of asymmetry in terrorist's attributes between government and terrorist on defense equilibrium, we propose a model in which the government chooses between disclosure (sequential game) and secrecy (simultaneous game) of her defense system. Our analysis shows that the government's first-mover advantage in a sequential game is considerable only when both government and terrorist share relatively similar valuation of targets. In contrast, we interestingly find that the government no longer benefits from the first-mover advantage by exposing her defense levels when the degree of divergence between government and terrorist valuation of targets is high. This is due to the robustness of defense system under secrecy, in the sense that all targets should be defended in equilibrium irrespective of how the terrorist valuation of targets is different to government. We identify two phenomena that lead to this result. First, when the terrorist holds a significantly higher valuation of targets than the government's belief, the government may waste her budget in a sequential game by over-investing on the high-valued targets. Second, when the terrorist holds a significantly lower valuation of targets, the government may incur a higher expected damage in a sequential game because of not defending the low-valued targets. Finally, we believe that this paper provides some novel insights to homeland security resource allocation problems.